Finite Group Databasebeta

← C47×#18950 #26058648

Subgroups — C47×#18950 #26058648

Order 12032.

824 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3556C211yesmaximal, characteristic, complemented
2C47×#3246C211yesmaximal, characteristic
3C47×#3228C211yesmaximal, characteristic
4C47×#3216C211yesmaximal, characteristic
5C47×#1653C212yesmaximal, complemented
6C47×#1648C212yesmaximal, complemented
7C47×#1626C212yesmaximal, complemented
8C47×#1626C212yesmaximal, complemented
9C47×#1552C211yesmaximal, characteristic, complemented
10C47×#1497C211yesmaximal, characteristic, complemented
11C47×#1481C211yesmaximal, characteristic, complemented
12C47×#564—22no—
13C47×#557—21no—
14C47×#557—21no—
15C47×#557—21no—
16C47×#557—21no—
17C47×#557C2212yes—
18C47×#557C2212yes—
19C47×#541—22no—
20C47×#541—22no—
21C47×#541—22no—
22C47×#533C2211yescharacteristic
23C47×#533C2211yescharacteristic
24C47×#533C2211yescharacteristic
25C47×#532C2211yescharacteristic
26C47×#500C2211yescharacteristic
27C47×#498C2211yescharacteristic
28C47×#497—21no—
29C47×#489—21no—
30C47×#486C2211yescharacteristic
31C47×#486C2211yescharacteristic
32C47×#482—22no—
33C47×#478—22no—
34C47×#476—21no—
35C47×#475C2212yes—
36C47×#465—22no—
37C47×#462C2212yes—
38C47×#461—21no—
39C47×#460C2212yes—
40C47×#460C2212yes—
41C47×#452—22no—
42C47×#432C2211yescharacteristic
43C47×#431C2211yescharacteristic
44C2×C4⋊C8×C47C2211yescharacteristic
45C47×#332C2212yes—
46C47×#332C2212yes—
47C47×Q8⋊C8C2212yes—
48C47×Q8⋊C8C2212yes—
49C47×Q8⋊C8C2212yes—
50C47×Q8⋊C8C2212yes—
51C2×#41×C47—21no—
52C2×Q16×C47—22no—
53C2×SD16×C47—22no—
54C2×SD16×C47—22no—
55C22×C8×C47—21no—
56C4⋊Q8×C47—22no—
57C4⋊Q8×C47—22no—
58C4⋊Q8×C47—22no—
59C4⋊Q8×C47D411yescharacteristic
60C4⋊Q8×C47D411yescharacteristic
61C4⋊Q8×C47D411yescharacteristic
62C4⋊Q8×C47D411yescharacteristic
63C4⋊Q8×C47C2311yescharacteristic
64C4⋊Q8×C47C2311yescharacteristic
65C4⋊Q8×C47C2311yescharacteristic
66#127×C47C2311yescharacteristic
67#126×C47—24no—
68#126×C47—24no—
69#125×C47—22no—
70#125×C47—24no—
71#125×C47—24no—
72#125×C47—24no—
73#125×C47—24no—
74#125×C47—22no—
75#125×C47—22no—
76#125×C47—24no—
77#125×C47—24no—
78#125×C47—21no—
79#125×C47—21no—
80#125×C47D412yes—
81#124×C47—21no—
82C22⋊Q8×C47—21no—
83C22⋊Q8×C47—21no—
84C22⋊Q8×C47—21no—
85C22⋊Q8×C47—21no—
86C22⋊Q8×C47D412yes—
87C22⋊Q8×C47D412yes—
88#121×C47—21no—
89#121×C47—21no—
90C4×Q8×C47—22no—
91C4×Q8×C47—22no—
92C4×Q8×C47—22no—
93C4×Q8×C47—22no—
94C4×Q8×C47—22no—
95C4×Q8×C47—22no—
96C4×Q8×C47—21no—
97C4×Q8×C47—21no—
98C4×Q8×C47—21no—
99C4×Q8×C47—21no—
100C4×Q8×C47C2312yes—
101C4×Q8×C47C2312yes—
102C4×D4×C47—21no—
103C4×D4×C47—21no—
104#117×C47—21no—
105#117×C47—21no—
106#117×C47D412yes—
107C2×C42×C47C2311yescharacteristic
108#107×C47—22no—
109#106×C47—22no—
110#106×C47—22no—
111C4⋊C8×C47—21no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47C2312yes—
114C4⋊C8×C47C2312yes—
115#103×C47—22no—
116#103×C47—22no—
117#102×C47—22no—
118#102×C47—22no—
119#102×C47—22no—
120#102×C47—22no—
121C22⋊C8×C47—21no—
122C22⋊C8×C47—21no—
123#97×C47—21no—
124C4×C8×C47C2311yescharacteristic
125C4×C8×C47C2311yescharacteristic
126#41×C47—82no—
127C2×Q8×C47—21no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47—21no—
131C2×Q8×C47—21no—
132C2×Q8×C47C2×D412yes—
133C2×Q8×C47C2×D412yes—
134C2×D4×C47—21no—
135C2×D4×C47—21no—
136C2×D4×C47—21no—
137C2×D4×C47—41no—
138C22×C4×C47—41no—
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142Q16×C47—82no—
143SD16×C47—82no—
144SD16×C47—82no—
145C2×C8×C47—22no—
146C2×C8×C47—22no—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
149C2×C8×C47—81no—
150C4⋊C4×C47—24no—
151C4⋊C4×C47—24no—
152C4⋊C4×C47—24no—
153C4⋊C4×C47—24no—
154C4⋊C4×C47—24no—
155C4⋊C4×C47—24no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—22no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47C2×D412yes—
173C4⋊C4×C47C2×D412yes—
174C4⋊C4×C47C2×D412yes—
175C4⋊C4×C47C2×D412yes—
176C22⋊C4×C47—22no—
177C22⋊C4×C47—22no—
178C22⋊C4×C47—22no—
179C22⋊C4×C47—41no—
180C22⋊C4×C47—41no—
181C42×C47—24no—
182C42×C47—24no—
183C42×C47—22no—
184C42×C47—22no—
185C42×C47—22no—
186C42×C47C2×D411yescharacteristic
187C42×C47C2×D411yescharacteristic
188C42×C47C2×D411yescharacteristic
189C42×C47C2411yescharacteristic
190C23×C47—41no—
191C23×C47#12011yescharacteristic
192Q8×C47—22no—
193Q8×C47—22no—
194Q8×C47—22no—
195Q8×C47—22no—
196Q8×C47—42no—
197Q8×C47—42no—
198Q8×C47—42no—
199Q8×C47—41no—
200Q8×C47—41no—
201Q8×C47—42no—
202D4×C47—42no—
203D4×C47—41no—
204D4×C47—42no—
205D4×C47—41no—
206D4×C47—82no—
207C2×C4×C47—21no—
208C2×C4×C47—22no—
209C2×C4×C47—21no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—82no—
219C2×C4×C47#12011yescharacteristic
220C2×C4×C47#12011yescharacteristic
221C2×C4×C47#12011yescharacteristic
222C2×C4×C47C22×D411yescharacteristic
223C2×C4×C47C22×D411yescharacteristic
224C2×C4×C47C22×D411yescharacteristic
225C8×C47—41no—
226C8×C47—41no—
227C8×C47—42no—
228C8×C47—42no—
229#18950C4711yesmaximal, characteristic, direct product factor, Sylow
230C22×C47—21no—
231C22×C47—21no—
232C22×C47—21no—
233C22×C47—81no—
234C22×C47—81no—
235C22×C47—81no—
236C22×C47C2×#12011yescharacteristic
237C4×C47—21no—
238C4×C47—21no—
239C4×C47—21no—
240C4×C47—21no—
241C4×C47—42no—
242C4×C47—42no—
243C4×C47—42no—
244C4×C47—42no—
245C4×C47—42no—
246C4×C47—42no—
247C4×C47—81no—
248C4×C47#57712yes—
249C4×C47#57711yescharacteristic
250C4×C47#57811yescharacteristic
251#3556C2×C4711yescharacteristic, complemented
252#3246C2×C4711yescharacteristic
253#3228C2×C4711yescharacteristic
254#3216C2×C4711yescharacteristic
255#1653C2×C4712yescomplemented
256#1648C2×C4712yescomplemented
257#1626C2×C4712yescomplemented
258#1626C2×C4712yescomplemented
259#1552C2×C4711yescharacteristic, complemented
260#1497C2×C4711yescharacteristic, complemented
261#1481C2×C4711yescharacteristic, complemented
262C2×C47—41no—
263C2×C47—161no—
264C2×C47#301011yescharacteristic
265C2×C47#301311yescharacteristic
266C2×C47#302011yescharacteristic
267#564—22no—
268#557—21no—
269#557—21no—
270#557—21no—
271#557—21no—
272#557C22×C4712yes—
273#557C22×C4712yes—
274#541—22no—
275#541—22no—
276#541—22no—
277#533C22×C4711yescharacteristic
278#533C22×C4711yescharacteristic
279#533C22×C4711yescharacteristic
280#532C22×C4711yescharacteristic
281#500C22×C4711yescharacteristic
282#498C22×C4711yescharacteristic
283#497—21no—
284#489—21no—
285#486C22×C4711yescharacteristic
286#486C22×C4711yescharacteristic
287#482—22no—
288#478—22no—
289#476—21no—
290#475C22×C4712yes—
291#465—22no—
292#462C22×C4712yes—
293#461—21no—
294#460C22×C4712yes—
295#460C22×C4712yes—
296#452—22no—
297#432C22×C4711yescharacteristic
298#431C22×C4711yescharacteristic
299C2×C4⋊C8C22×C4711yescharacteristic
300#332C22×C4712yes—
301#332C22×C4712yes—
302Q8⋊C8C22×C4712yes—
303Q8⋊C8C22×C4712yes—
304Q8⋊C8C22×C4712yes—
305Q8⋊C8C22×C4712yes—
306C47#1895011yescharacteristic, direct product factor, Sylow
307C2×#41—21no—
308C2×Q16—22no—
309C2×SD16—22no—
310C2×SD16—22no—
311C22×C8—21no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8D4×C4711yescharacteristic
316C4⋊Q8D4×C4711yescharacteristic
317C4⋊Q8D4×C4711yescharacteristic
318C4⋊Q8D4×C4711yescharacteristic
319C4⋊Q8C23×C4711yescharacteristic
320C4⋊Q8C23×C4711yescharacteristic
321C4⋊Q8C23×C4711yescharacteristic
322#127C23×C4711yescharacteristic
323#126—24no—
324#126—24no—
325#125—22no—
326#125—24no—
327#125—24no—
328#125—24no—
329#125—24no—
330#125—22no—
331#125—22no—
332#125—24no—
333#125—24no—
334#125—21no—
335#125—21no—
336#125D4×C4712yes—
337#124—21no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8D4×C4712yes—
343C22⋊Q8D4×C4712yes—
344#121—21no—
345#121—21no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8C23×C4712yes—
357C4×Q8C23×C4712yes—
358C4×D4—21no—
359C4×D4—21no—
360#117—21no—
361#117—21no—
362#117D4×C4712yes—
363C2×C42C23×C4711yescharacteristic
364#107—22no—
365#106—22no—
366#106—22no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8C23×C4712yes—
370C4⋊C8C23×C4712yes—
371#103—22no—
372#103—22no—
373#102—22no—
374#102—22no—
375#102—22no—
376#102—22no—
377C22⋊C8—21no—
378C22⋊C8—21no—
379#97—21no—
380C4×C8C23×C4711yescharacteristic
381C4×C8C23×C4711yescharacteristic
382#41—82no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8C2×D4×C4712yes—
389C2×Q8C2×D4×C4712yes—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—41no—
394C22×C4—41no—
395C22×C4C2×D4×C4711yescharacteristic
396C22×C4C2×D4×C4711yescharacteristic
397C22×C4C2×D4×C4711yescharacteristic
398Q16—82no—
399SD16—82no—
400SD16—82no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—81no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4C2×D4×C4712yes—
429C4⋊C4C2×D4×C4712yes—
430C4⋊C4C2×D4×C4712yes—
431C4⋊C4C2×D4×C4712yes—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C42—24no—
438C42—24no—
439C42—22no—
440C42—22no—
441C42—22no—
442C42C2×D4×C4711yescharacteristic
443C42C2×D4×C4711yescharacteristic
444C42C2×D4×C4711yescharacteristic
445C42C24×C4711yescharacteristic
446C23—41no—
447C23#120×C4711yescharacteristic
448Q8—22no—
449Q8—22no—
450Q8—22no—
451Q8—22no—
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—41no—
456Q8—41no—
457Q8—42no—
458D4—42no—
459D4—41no—
460D4—42no—
461D4—41no—
462D4—82no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—82no—
475C2×C4#120×C4711yescharacteristic
476C2×C4#120×C4711yescharacteristic
477C2×C4#120×C4711yescharacteristic
478C2×C4C22×D4×C4711yescharacteristic
479C2×C4C22×D4×C4711yescharacteristic
480C2×C4C22×D4×C4711yescharacteristic
481C8—41no—
482C8—41no—
483C8—42no—
484C8—42no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C2×#120×C4711yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—81no—
503C4C47×#57712yes—
504C4C47×#57711yescharacteristic
505C4C47×#57811yescharacteristic
506C2—41no—
507C2—161no—
508C2C47×#301011yescharacteristic
509C2C47×#301311yescharacteristic
510C2C47×#302011yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C47×#3556C2semidirect
5. C47×#1653C2semidirect
6. C47×#1648C2semidirect
7. C47×#1626C2semidirect
8. C47×#1626C2semidirect
9. C47×#1552C2semidirect
10. C47×#1497C2semidirect
11. C47×#1481C2semidirect
229. #18950C47direct (N × H)
251. #3556C2×C47semidirect
255. #1653C2×C47semidirect
256. #1648C2×C47semidirect
257. #1626C2×C47semidirect
258. #1626C2×C47semidirect
259. #1552C2×C47semidirect
260. #1497C2×C47semidirect
261. #1481C2×C47semidirect
306. C47#18950direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C47×#35562
C47×#32462
C47×#32282
C47×#32162
C47×#16532
C47×#16482
C47×#16262
C47×#15522
C47×#14972
C47×#14812
#1895047